Barack Obama’s decision to wade into the EU referendum debate has riled Eurosceptics. But they risk doing more harm than good if they allow anger to govern their response.

In the media over the last couple of days a few distinct approaches have started to emerge, and some are much more promising than others.

The first, broadly unhelpful school comprises those who chose to attack Obama directly. This could be because he’s a “bad President”, or playing on the allegation that the President is “anti-British”, as Boris does to an extent in his article in today’s Sun.

Such attacks seem likely to be counter-productive. Most Britons – and likely the overwhelming majority of low-engagement, undecided voters – do not know enough about American politics for arguments based on the shortcomings of the Obama administration to have any cut through.

The ‘unceremonious’ return of a bust of Churchill on the President’s first day in office is, likewise, not likely to greatly irritate the sort of person who doesn’t yet have a firm idea on the EU.

More effective responses all seem to centre on a (polite, measured) rebuke of Obama’s “do as I say, not as I do” attitude.

For example, the better sections of the Mayor’s Sun article were those that riffed on the President’s soaring, optimistic rhetoric from 2008, contrasting the politics of “Yes we can!” with his participation in the doom-laden ‘Remain’ campaign.

Iain Duncan Smith has also made the papers today by pointing out that the United States would never consent to an EU-style arrangement itself, especially not one where it was serially outvoted.

This point is taken further by John O’Sullivan, once senior policy aide to Margaret Thatcher, in pre-eminent American conservative magazine National Review. He points out that Obama is doing his job, which is to advocate for US interests – but that these interests don’t always overlap with British interests.

Given that Obama is relatively popular in Britain, this sort of approach seems far more likely to work: claim that your campaign is inspired by his best bits (the hope-and-change positivity) whilst repeatedly – but reasonably – highlighting the inconsistencies in his position and their root in the fact that the place America wants Britain is not the best place for Britain to be.

Fundamentally, it is about minimising any sense of contrast between a man many voters still think of as Mr Optimism and the Leave campaign, instead suggesting that the desire for British independence is actually the positive step and laying the difference of opinion at the feet of the President’s need to put US interests firsts.

Ideally, from their perspective, the Brexiteers would also find a way to highlight the contrast between Obama’s politics – at least, his 2008 politics which British voters might remember – and the overwhelming negativity on the Remain side.

The alternative, which is to snarlingly demand that he keep his foreign nose out, couldn’t be better designed to confirm the ‘nasty’ caricature of the Leave campaign.